In this paper, we propose a procedure for quantifying and reducing uncertainties that impact numerical simulations involved in the estimation of the fatigue of a wind turbine structure. The present study generalizes a previous work carried out by the authors proposing to quantify and to reduce uncertainties that affect the properties of a wind turbine model by combining a global sensitivity analysis and a recursive Bayesian filtering approach. We extend the procedure to include the uncertainties involved in the modeling of a synthetic wind field. Unlike the model properties having a static or slow time-variant behavior, the parameters related to the external solicitation have a non-explicit dynamic behavior, which must be taken into account during the recursive inference. A non-parametric data-driven approach to approximate the non-explicit dynamic of the inflow related parameters is used. More precisely, we focus on data assimilation methods combining a nearest neighbor or an analog sampler with a stochastic filtering method such as the ensemble Kalman filter. The so-called data-driven data assimilation approach is used to recursively reduce the uncertainties that affect the parameters related to both model properties and wind field. For the approximation of the non-explicit dynamic of the wind inflow related parameters, in situ observations obtained from a light detection and ranging system and a cup-anemometer device are used. For the data-assimilation procedure, synthetic data simulated from the aero-servo-elastic numerical model are considered. The next investigations will be to verify the procedure with real in situ data.
References
1.
Aanonsen
, S. I.
, Nævdal
, G.
, Oliver
, D. S.
, Reynolds
, A. C.
, Vallès
, B.
et al., “The ensemble Kalman filter in reservoir engineering: A review
,” SPE J.
14
, 393
–412
(2009
).2.
Alexander
, R.
, Zhao
, Z.
, Székely
, E.
, and Giannakis
, D.
, “Kernel analog forecasting of tropical intraseasonal oscillations
,” J. Atmos. Sci.
74
, 1321
–1342
(2017
).3.
Ayet
, A.
and Tandeo
, P.
, “Nowcasting solar irradiance using an analog method and geostationary satellite images
,” Sol. Energy
164
, 301
–315
(2018
).4.
Bertino
, L.
, Evensen
, G.
, and Wackernagel
, H.
, “Sequential data assimilation techniques in oceanography
,” Int. Stat. Rev.
71
, 223
–241
(2003
).5.
Bocquet
, M.
, Farchi
, A.
, and Malartic
, Q.
, “Online learning of both state and dynamics using ensemble Kalman filters
,” arXiv:2006.03859 (2020
).6.
Brown
, S. D.
, “The Kalman filter in analytical chemistry
,” Anal. Chim. Acta
181
, 1
–26
(1986
).7.
Brunton
, S. L.
, Proctor
, J. L.
, and Kutz
, J. N.
, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems
,” Proc. Natl. Acad. Sci.
113
, 3932
–3937
(2016
).8.
Chau
, T. T. T.
, Ailliot
, P.
, and Monbet
, V.
, “An algorithm for non-parametric estimation in state–space models
,” Comput. Stat. Data Anal.
153
, 107062
(2021
).9.
Chen
, L.
, “Curse of dimensionality
,” in Encyclopedia of Database Systems
, edited by L.
Liu
and M. T.
Özsu
(Springer US
, Boston, MA
, 2009
), pp. 545
–546
.10.
Damblin
, G.
, Couplet
, M.
, and Iooss
, B.
, “Numerical studies of space-filling designs: Optimization of Latin Hypercube Samples and subprojection properties
,” J. Simul.
7
, 276
–289
(2013
).11.
Dimitrov
, N.
, Natarajan
, A.
, and Kelly
, M.
, “Model of wind shear conditional on turbulence and its impact on wind turbine loads
,” Wind Energy
18
, 1917
–1931
(2015
).12.
Dimitrov
, N.
, Natarajan
, A.
, and Mann
, J.
, “Effects of normal and extreme turbulence spectral parameters on wind turbine loads
,” Renewable Energy
101
, 1180
–1193
(2017
).13.
Dobre
, S.
, Bastogne
, T.
, Profeta
, C.
, Barberi-Heyob
, M.
, and Richard
, A.
, “Limits of variance-based sensitivity analysis for non-identifiability testing in high dimensional dynamic models
,” Automatica
48
, 2740
–2749
(2012
).14.
Durbin
, J.
and Koopman
, S. J.
, Time Series Analysis by State Space Methods
(Oxford University Press
, 2012
).15.
Efron
, B.
, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods
,” Biometrika
68
, 589
–599
(1981
).16.
Evensen
, G.
, “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
,” J. Geophys. Res.: Oceans
99
, 10143
–10162
, (1994
).17.
Evensen
, G.
, “The ensemble Kalman filter: Theoretical formulation and practical implementation
,” Ocean Dyn.
53
, 343
–367
(2003
).18.
Evensen
, G.
, Data Assimilation: The Ensemble Kalman Filter
(Springer Science and Business Media
, 2009
).19.
Fablet
, R.
, Viet
, P.
, Lguensat
, R.
, and Chapron
, B.
, “Data-driven assimilation of irregularly-sampled image time series
,” in 2017 IEEE International Conference on Image Processing (ICIP)
(IEEE
, 2017
), pp. 4302
–4306
.20.
Friedman
, J. H.
, “On bias, variance, 0/1-loss, and the curse-of-dimensionality
,” Data Mining Knowl. Discovery
1
, 55
–77
(1997
).21.
Ginsbourger
, D.
, Picheny
, V.
, Roustant
, O.
, and Richet
, Y.
, “Kriging with heterogeneous nugget effect for the approximation of noisy simulators with tunable fidelity (krigeage avec effet de pépite hétérogène pour l'approximation de simulateurs bruités fidélité réglable)
,” in Proceedings of Joint Meeting of the Statistical Society of Canada and the Société Francaise de Statistique
(2008
).22.
Hamilton
, F.
, Berry
, T.
, and Sauer
, T.
, “Ensemble Kalman filtering without a model
,” Phys. Rev. X
6
, 011021
(2016
).23.
24.
Harvey
, A. C.
, Forecasting, Structural Time Series Models and the Kalman Filter
(Cambridge University Press
, 1990
).25.
26.
Hirvoas
, A.
, Prieur
, C.
, Arnaud
, E.
, Caleyron
, F.
, and Munoz Zuniga
, M.
, “Quantification and reduction of uncertainties in a wind turbine numerical model based on a global sensitivity analysis and a recursive Bayesian inference approach
,” Int. J. Numer. Methods Eng.
122
, 2528
(2021
).27.
Holierhoek
, J.
, Korterink
, H.
, van de Pieterman
, R.
, Rademakers
, L.
, and Lekou
, D.
, “Recommended practices for measuring in situ the ‘loads’ on drive train, pitch system and yaw system
,” in Energy Research Center of the Netherlands (ECN)
(2010
).28.
Houtekamer
, P. L.
, He
, B.
, and Mitchell
, H. L.
, “Parallel implementation of an ensemble Kalman filter
,” Mon. Weather Rev.
142
, 1163
–1182
(2014
).29.
Houtekamer
, P. L.
and Mitchell
, H. L.
, “A sequential ensemble Kalman filter for atmospheric data assimilation
,” Mon. Weather Rev.
129
, 123
–137
(2001
).30.
IEC
, IEC 61400-1, Wind Turbines-Part 1
(IEC
, 2005
).31.
IEC,
IEC 61400-1: 2019: Wind Energy Generation Systems-Part 1: Design Requirements
(IEC
, 2019
).32.
Iooss
, B.
, Janon
, A.
, Pujol
, G.
, with contributions from Broto
, B.
, Boumhaout
, K.
, Veiga
, S. D.
, Delage
, T.
, Fruth
, J.
, Gilquin
, L.
, Guillaume
, J.
, Le Gratiet
, L.
, Lemaitre
, P.
, Nelson
, B. L.
, Monari
, F.
, Oomen
, R.
, Rakovec
, O.
, Ramos
, B.
, Roustant
, O.
, Song
, E.
, Staum
, J.
, Sueur
, R.
, Touati
, T.
, and Weber
, F.
, see https://CRAN.R-project.org/package=sensitivity for “Sensitivity: Global Sensitivity Analysis of Model Outputs, r package version 1.16.0
” (2019
).33.
Jansen
, M. J.
, “Analysis of variance designs for model output
,” Comput. Phys. Commun.
117
, 35
–43
(1999
).34.
Jonkman
, B. J.
, “Turbsim user's guide: Version 1.50
,” Technical Report No. NREL/TP-500-46198
[National Renewable Energy Lab (NREL)
, Golden, CO
, 2009
].35.
Jonkman
, J. M.
and Buhl
, M. L.
, Jr. et al., Fast User's Guide
(National Renewable Energy Laboratory
, Golden, CO
, 2005
), Vol. 365
, p. 366
.36.
Julier
, S. J.
and Uhlmann
, J. K.
, “New extension of the Kalman filter to nonlinear systems
,” in Signal Processing, Sensor Fusion, and Target Recognition VI
(International Society for Optics and Photonics
, 1997
), Vol. 3068
, pp. 182
–193
.37.
Kaimal
, J. C.
, Wyngaard
, J. C.
, Izumi
, Y.
, and Coté
, O.
, “Spectral characteristics of surface-layer turbulence
,” Q. J. R. Meteorol. Soc.
98
, 563
–589
(1972
).38.
Kalman
, R. E.
, “A new approach to linear filtering and prediction problems
,” J. Basic Eng.
82
, 35
–45
(1960
).39.
Koukoura
, C.
, “Validated loads prediction models for offshore wind turbines for enhanced component reliability
,” Ph.D. thesis (Technical University of Denmark
, 2014
).40.
Lamboni
, M.
, Monod
, H.
, and Makowski
, D.
, “Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models
,” Reliab. Eng. Syst. Saf.
96
, 450
–459
(2011
).41.
Lguensat
, R.
, Tandeo
, P.
, Ailliot
, P.
, Pulido
, M.
, and Fablet
, R.
, “The analog data assimilation
,” Mon. Weather Rev.
145
, 4093
–4107
(2017
).42.
Lorenz
, E. N.
, “Atmospheric predictability as revealed by naturally occurring analogues
,” J. Atmos. Sci.
26
, 636
–646
(1969
).43.
Marrel
, A.
, Iooss
, B.
, Van Dorpe
, F.
, and Volkova
, E.
, “An efficient methodology for modeling complex computer codes with gaussian processes
,” Comput. Stat. Data Anal.
52
, 4731
–4744
(2008
).44.
Meyers
, M. A.
and Chawla
, K. K.
, Mechanical Behavior of Materials
(Cambridge University Press
, 2008
).45.
Pathak
, J.
, Hunt
, B.
, Girvan
, M.
, Lu
, Z.
, and Ott
, E.
, “Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach
,” Phys. Rev. Lett.
120
, 024102
(2018
).46.
Peterson
, L. E.
, “K-nearest neighbor
,” Scholarpedia
4
, 1883
(2009
).47.
Robertson
, A. N.
, Shaler
, K.
, Sethuraman
, L.
, and Jonkman
, J. M.
, “Sensitivity analysis of the effect of wind characteristics and turbine properties on wind turbine loads
,” Wind Energy Sci.
4
, 479
(2019a
).48.
Robertson
, A. N.
, Shaler
, K.
, Sethuraman
, L.
, and Jonkman
, J. M.
, “Sensitivity of uncertainty in wind characteristics and wind turbine properties on wind turbine extreme and fatigue loads
,” No. NREL/JA-5000-74246
[National Renewable Energy Lab. (NREL), Golden, CO, 2019b
].49.
Saranyasoontorn
, K.
, Manuel
, L.
, and Veers
, P.
, “On estimation of coherence in inflow turbulence based on field measurements
,” AIAA Paper No. 2004-1002, 2004
.50.
Simms
, D.
, Schreck
, S.
, Hand
, M.
, and Fingersh
, L. J.
, “NREL unsteady aerodynamics experiment in the NASA-Ames wind tunnel: A comparison of predictions to measurements
,” Technical Report No.
NREL/TP-500-29494 (National Renewable Energy Lab
., Golden, CO
, 2001
).51.
Snyder
, C.
and Zhang
, F.
, “Assimilation of simulated Doppler radar observations with an ensemble Kalman filter
,” Mon. Weather Rev.
131
, 1663
(2003
).52.
Sobol'
, I. M.
, “On sensitivity estimation for nonlinear mathematical models
,” Mat. Model.
2
, 112
–118
(1990
).53.
Solari
, G.
and Piccardo
, G.
, “Probabilistic 3-D turbulence modeling for gust buffeting of structures
,” Probab. Eng. Mech.
16
, 73
–86
(2001
).54.
Tandeo
, P.
, Ailliot
, P.
, Fablet
, R.
, Ruiz
, J.
, Rousseau
, F.
, and Chapron
, B.
, “The analog ensemble Kalman filter and smoother
,” in CI 2014: 4th International Workshop on Climate Informatics
(2014
).55.
Tandeo
, P.
, Ailliot
, P.
, Ruiz
, J.
, Hannart
, A.
, Chapron
, B.
, Cuzol
, A.
, Monbet
, V.
, Easton
, R.
, and Fablet
, R.
, “Combining analog method and ensemble data assimilation: Application to the Lorenz-63 chaotic system
,” in Machine Learning and Data Mining Approaches to Climate Science
(Springer
, 2015
), pp. 3
–12
.56.
Toth
, Z.
, “Long-range weather forecasting using an analog approach
,” J. Clim.
2
, 594
–607
(1989
).57.
Veldkamp
, H. F.
, Chances in Wind Energy: A Probalistic Approach to Wind Turbine Fatigue Design
(Delft University Wind Energy Research Institute
, 2006
).58.
Welch
, P.
, “The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
,” IEEE Trans. Audio Electroacoust.
15
, 70
–73
(1967
).59.
Wells
, C.
, The Kalman Filter in Finance
(Springer Science and Business Media
, 2013
), Vol. 32
.60.
Witcher
, D.
, “Uncertainty quantification techniques in wind turbine
,” oral presentation, DNV GL (2017
).61.
Wold
, S.
, Esbensen
, K.
, and Geladi
, P.
, “Principal component analysis
,” Chemometr. Intell. Lab. Syst.
2
, 37
–52
(1987
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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